What is the Dubins path?

Geometrically speaking, the shortest way to get from point A to point B is along a straight line. But what’s the shortest route if you have directional restrictions?

Suppose you have a car moving in a 2D plane and a restriction on how sharply it can turn, a maximum curvature. You’re in point A facing in direction A’, and need to arrive at point B from direction B’. What’s the shortest route? It’s along a Dubins path.

In general, the Dubins path consists of three segments – either a turn, a straight line and another turn, or three turns in alternating directions. (All turns are made at the maximum curvature.)

Why is it important?

I love the Dubins path – it’s an elegant solution to what looks like a fairly simple problem. It has an obvious application in path planning – if you’re designing an autonomous vehicle, you probably want it to follow a Dubins path at least some of the time.

Who was Lester Dubins?

Lester Dubins (1920-2010) was born in New York and served in the USAF during the Second World War. He then worked on radar research for several years before undertaking graduate study at the University of Chicago. After receiving his PhD in 1955, he worked at the IAS in Princeton and at Carnegie Mellon before joining UC Berkeley for the rest of his career. (Famously, he won a court case in the early 1990s to allow him to come out of retirement.) He eventually retired on his own terms in 2004 and died six years later.

He’s not best-known for his work on paths: rather, he was a renowned probability theorist and wrote (with Leonard Jimmie Savage) the marvellously-titled How To Gamble If You Must (Inequalities for Stochastic Processes). He’s also partly responsible for the Dubins-Spanier theorems on fair division.